No, they didn't. I know Kofi was supposed to win it in 2008, but Randy threw a fit because Kofi forgot the finish to a triple threat between them and John Cena, leading to Kofi's push being derailed. Jeff was supposed to win one too at some point, don't remember when. As far as I know, Becky has never been in talks for a MITB win
Becky has never won one. Jeff, was suppose to win in 2008. But, got suspended, and they gave it to Punk. Ended up winning the wwe title that year anyway. Kofi has also been involved with the match. But, never won. Big E did.